Inthe present paper we have considered the mapwhere , are parameters. The map was originally proposed by Maynard Smith [17] for study of population growth. We have shown how chaos creep into the model. We have used the techniques of Lyapunov exponent, time series analysis, Fourier spectra, Bifurcation diagram, correlation and embedding dimension etc. to draw our conclusions. Further, we have shown how the 'periodic proportional pulse' method can be used to control the chaos generated in the system.
We have analyzed a model of Lotka-Volterra type interacting between immune cell-tumour cell-normal cells, where control policy is applied in terms of targeted chemotherapy. We determined conditions for the local stability of all the equilibrium points and global stability condition for the tumour free equilibrium point, including the feasibility of the solution. Further, we have discussed the possibility of Hopf bifurcation at each equilibrium point. Numerical simulation was carried out to observe the qualitative behaviour of the system as the control parameter is varied.
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